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Jovian magnetospheric plasma irradiates the surface of Ganymede and is postulated to be the primary agent that changes the surface brightness of Ganymede, leading to asymmetries between polar and equatorial regions as well as between the trailing and leading hemispheres. As impinging ions sputter surface constituents as neutrals, ion precipitation patterns can be remotely imaged using the Energetic Neutral Atoms (ENA) measurement technique. Here we calculate the expected sputtered ENA flux from the surface of Ganymede to help interpret future observations by ENA instruments, particularly the Jovian Neutrals Analyzer (JNA) onboard the JUpiter ICy moon Explorer (JUICE) spacecraft. We use sputtering models developed based on laboratory experiments to calculate sputtered fluxes of H2O, O2, and H2. The input ion population used in this study is the result of test particle simulations using electric and magnetic fields from a hybrid simulation of Ganymede's environment. This population includes a thermal component (H+ and O+ from 10 eV to 10 keV) and an energetic component (H+, O++, and S+++ from 10 keV to 10 MeV). We find a global ENA sputtering rate from Ganymede of 1.42 × 1027 s−1, with contributions from H2, O2, and H2O of 34%, 17%, and 49% respectively. We also calculate the energy distribution of sputtered Energetic Neutral Atoms (ENAs), give an estimate of a typical JNA count rate at Ganymede, and investigate latitudinal variations of sputtered fluxes along a simulated orbit track of the JUICE spacecraft. Our results demonstrate the capability of the JNA sensor to remotely map ion precipitation at Ganymede.